How do I set influence radius to a specific size?
As with most operations in blender, the redo panel (F9 in 2.8+ keymap, or  F6 for 2.7 keymap) provides the ability to adjust the operator immediately after it is run. Keep in mind, if you use another operator (scale, translate, etc before adjusting prop edit), then the ability to adjust is gone.
See the gif below: